The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making

•An extended TOPSIS method is proposed using an inclusion comparison approach.•Multi-criteria group decision-making problems are addressed in the IVIFS context.•A modified IIHA operation is presented using inclusion-based IIOWA operations.•Inclusion-based closeness coefficients are provided in the new TOPSIS model.•The feasibility is illustrated by a medical group decision-making problem.

The technique for order preference by similarity to ideal solution (TOPSIS) method is a well-known compromising method for multiple criteria decision analysis. This paper develops an extended TOPSIS method with an inclusion comparison approach for addressing multiple criteria group decision-making problems in the framework of interval-valued intuitionistic fuzzy sets. Considering the relative agreement degrees and the importance weights of multiple decision makers, this paper presents a modified hybrid averaging method with an inclusion-based ordered weighted averaging operation for forming a collective decision environment. Based on the main structure of the TOPSIS method, this paper utilizes the concept of inclusion comparison possibilities to propose a new index for an inclusion-based closeness coefficient for ranking the alternatives. Additionally, two optimization models are established to determine the criterion weights for addressing situations in which the preference information is completely unknown or incompletely known. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a medical group decision-making problem.

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